Velocity Dispersions in Clusters of Galaxies

Summary Estimate the gravitational mass of the Coma Cluster of Galaxies to compare to mass of hot gas (seen in X-ray images) and stars found in the member galaxies.

Background - Galaxies are not merely strewn randomly throughout space. Instead, they often come in groups or clusters ranging from small associations of a few large galaxies to giant clusters which contain thousands of galaxies. Our own Milky Way galaxy is a member of a small group called the Local Group, consisting of the Milky Way, the two other large spirals M31 (the Andromeda galaxies) and M33 (the Pinwheel), and a number of small satellite galaxies.

Figure 1: The Coma Cluster of Galaxies
(National Optical Astronomy Observatory)

The nearest large cluster of galaxies is the Virgo Cluster, approximately 18 million parsecs (Mpc) away. At the center of the Virgo Cluster is the giant elliptical galaxy M87. Even further away is the dense, massive Coma Cluster (100 Mpc distant).

Galaxies within clusters are bound together by their mutual gravitational pull. Unlike the rest of the Universe, which expands with the cosmic expansion since the Big Bang, galaxies in clusters do not expand away from each other, but rather orbit around the cluster center on timescales of billions of years. As they orbit inside the cluster, galaxies often pass by each other enough to distort one another by their gravitational pull. In extreme cases, galaxies can actually capture each other and merge together, in a process which transforms spiral galaxies into elliptical galaxies. As these interactions between cluster galaxies occur, the galaxy population is slowly changed from the spiral-dominated galaxy population (observed outside of clusters) into the elliptical dominated populations found in rich clusters.

Clusters of galaxies are interesting laboratories for studying galaxy evolution, and can also tell us much about the evolution of the Universe in general. The rate at which clusters form and evolve depends on the density of matter in the Universe -- if the density is low, there is not enough mass to keep clusters forming continuously throughout cosmic history. By studying clusters we can learn about how the Universe itself evolves.

Clusters also tell us about the mysterious dark matter which permeates the Universe. By studying the velocities of galaxies in clusters, we can measure the amount of mass contained inside the cluster. Comparing this "dynamical mass" to the amount of mass we infer just by counting galaxies, we find that much of the mass in clusters is not contained within the galaxies themselves. Even when we account for the hot intracluster gas (which emits X-rays, not visible light), we still come up with only 10% of the total mass we infer from the galaxy velocities. The "missing mass," comprising 90% of the mass in galaxy clusters, is the mysterious dark matter which we still do not understand.

Measuring the Mass of Coma – Just as the velocities of stars orbiting a galaxy tell us the mass of the galaxy, so do the motions of galaxies in a cluster tell us the mass of the cluster. Since there is no central massive core to a galaxy cluster, however, galaxies in a cluster move more like a swarm of bees than the stately rotation of a spiral galaxy. To measure the mass of a cluster of galaxies, astronomers must measure the radial velocity of many galaxies in the cluster to determine the cluster's velocity dispersion.

The velocities of individual galaxies are measured from spectra using the Doppler Effect. Remember, however, that the cluster of galaxies is itself receding from us. The width of the histogram tells us the spread in velocities, or the velocity dispersion, while the average velocity tells us about how fast the cluster as a whole is moving away from us due to the cosmological expansion of the universe.

The Coma Velocity Dispersion – Log onto the computer, open a browser, and load the JavaLab at http://burro.astr.cwru.edu/JavaLab/clusters/ClustersApplet.html.

In this JavaLab, we will use the velocities and spatial distribution of galaxies in clusters to get an estimate of the dynamical mass of clusters.

Select the Coma Cluster from the pulldown menu at the upper right of the window.

An image of the Coma Cluster will appear in this pane. If the image is too large to be viewed in the pane, you can use the scroll bars to view the hidden portions of the image.
When you move your mouse over a galaxy in the image, information regarding that galaxy will appear in the small window to the right.
When you click on a galaxy, a circle will be drawn around it, indicating that it has been added to the data set for analysis. Clicking the galaxy again will toggle its selection off. Holding down CONTROL while clicking will deselect all of the galaxies.

Almost all of the objects visible in the image are galaxies in the Coma Cluster. A handful of Milky Way stars are also visible – the objects with points, such as the bright star near the right edge of the frame. Select about 50 galaxies. You can switch back and forth between the Analyze and the Select frame to see how your histogram is building up.

When you have selected a good sample of galaxies, click the "analyze" button to switch to the analysis screen, where you can analyze the cluster based upon the galaxies you have chosen.

You may wish to set lower and upper limits for the radial velocities to be included in the calculation to eliminate outlying velocities. Some few galaxies are either foreground or background objects that are not members of the Coma Cluster.

Also enter a value for the Hubble Constant (use Ho=72 km s-1 Mpc-1, which will be used to calculate the distance to Coma.

Click the Calculate button to display the cluster distance, luminosity, size (half-light radius), gravitational mass, and mass to light ratio.

The Coma Mass Budget - If we measure the dynamical mass of the Coma Cluster from the velocity dispersion, we get something like

Mgrav ~ 1015 MSun

The Java applet seems to give a value closer to 1014 MSun, so if that is what you get, use your value. The discrepancy seems to be due to the relatively simple dynamical model used to estimate the mass. The total visible luminosity of the Coma cluster galaxies is

Ltot ~ 1012 Lsun

And if we say that each galaxy has a mass-to-light ratio (including both stars and any dark matter within the galaxy) of 10, this says that the galaxies have a total mass of

Mgal ~ 10 x 1012 = 1013Msun

That's just a fraction of the total mass!

But Coma also contains hot gas distributed throughout the cluster which shines not in visible light, but in X-rays. Using X-ray satellites, we can observe and estimate the mass of this gas; it turns out to be about

Mx ~ 1014 Msun

A view of the Coma Cluster in optical light (left) and at X-ray (right, from Chandra) wavelengths

X-ray observations of the Coma Cluster of Galaxies indicate that the space within the cluster contains not only galaxies, but hot gas that emits X-rays and can be detected with X-ray telescopes. Coma contains six times more mass in hot gas disbursed throughout the cluster than is in the visible galaxies. But even with the hot gas, the visible mass (hot gas plus galaxies) is still much less than the gravitational mass of the cluster measured using the velocity dispersion of the galaxies.

Based on arguments like this, astronomers have been led to the conclusion that most of the mass in galaxy clusters -- and in the universe in general -- remains unobserved, the strange "dark matter" that we still don't understand...

This exercise is based on a JavaLab developed by Chris Mihos at Case Western Reserve University, and has been adapted for use in the Workshop "Exploring the Dark Universe" at Indiana University.